Units and Measurements

The percentage error in the calculated volume of a sphere, if there is 2% error in its diameter measurement, is ______.

Match List - I with List - II. List - I: A. Boltzmann constant; B. Stefan's constant; C. Planck's constant; D. Gravitational constant. List - II: I. $[\mathrm{M^{-1}L^3T^{-2}}]$; II. $[\mathrm{ML^2T^{-1}}]$; III. $[\mathrm{ML^2T^{-2}K^{-1}}]$; IV. $[\mathrm{ML^0T^{-3}K^{-4}}]$. Choose the correct answer from the options given below :

Dimensions of universal gravitational constant $(G)$ in terms of Planck's constant $(h)$, distance $(L)$, mass $(M)$ and time $(T)$ are ______.

Match the LIST-I with LIST-II. LIST-I: A. Planck's constant; B. Stopping potential; C. Work function; D. Threshold frequency. LIST-II: I. $\mathrm{ML^2T^{-2}}$; II. $\mathrm{T^{-1}}$; III. $\mathrm{ML^2T^{-1}}$; IV. $\mathrm{ML^2T^{-3}A^{-1}}$. Choose the correct answer from the options given below:

$L$, $C$ and $R$ represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula $\mathrm{M}\,\mathrm{L}^2\,\mathrm{T}^{-4}\,\mathrm{A}^{-2}$ corresponds to _________.

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as 10 V and 5 A, respectively. The least counts of voltmeter and ammeter are 500 mV and 200 mA, respectively. The estimated error in the resistance measurement is ______ $\Omega$

The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m$, $l$ and $d$ are $97.42\pm0.02$ g, $8.35\pm0.05$ mm and $20.20\pm0.02$ mm, respectively. Calculated percentage fractional error in $\rho$ is ________.

The potential energy of a particle changes with distance $x$ from a fixed origin as $V=\frac{A\sqrt x}{x+B}$, where $A$ and $B$ are constant with appropriate dimensions. The dimensions of $AB$ are ________.

A new unit ($\alpha$) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $\alpha$ units if light takes 6 min. 40 s to cover this distance ?

Consider the equation $H=\frac{x^p\epsilon^qE^r}{t^s}$, where $H$ = magnetic field; $E$ = electric field, $\epsilon$ = permittivity, $x$ = distance, $t$ = time. The values of $p$, $q$, $r$ and $s$ respectively are :